Because of its large dissociation energy and the relatively high
abundance of its constituent atoms, carbon monoxide in its several
isotopic forms is observed in a variety of astrophysical sources.
Since many of these sources are quite hot (T $>$\ 7000 K), the
molecular emissions can be observed from highly excited vibrational
levels that may or may not be in LTE.
Improvements in the electric dipole moment function (EDMF) by
Chackerian, et al. [Can. J. Phys., 62, 1579 (1984)]
and recent advances in calculating wave functions by Goorvitch and Galant
[J. Quant. Spectrosc. Rad. Transf., 47, 391 (1992)]
make it worthwhile to recalculate the rovibrational transition moments
for all the transitions with
$v \leq$\ 20, $J \leq$\ 150 and $\Delta v$\ = +1, +2, and +3
for the $^{12}$C$^{16}$O and $^{13}$C$^{16}$O $X\ ^{1}
\Sigma^{+}$\ states.
These calculated transition moments combined with
highly accurate term values and transition frequencies reported
by Farrenq, et al. [ J. Molec. Spectrosc., 149,
1579 (1991)] allow the calculation of the Einstein
A values, $gf$\ values, and line strengths.
We observe that there is intensity enhancement for
the P transitions at the expense of the R transitions for
$\Delta v$\ = +1. This enhancement can be as large as 40\% at
the highest $J$.
For the $\Delta v$ = +2 and +3 transitions, the R transitions
are enhanced by as much as a factor of 2.75 and 10 at the
highest J, respectively.
The P transitions exhibit minor decreases. The expectation
value of the transition moments are given as a polynomial expansion
in terms of the parameter $m$\ which is defined in terms of the lower
state angular momentum quantum number $J$. These results are
derived using orthogonal polynomials which are tested for being
statistically significant.